Agriculture Reference
In-Depth Information
Table 8.4 Determination of the no. of classes according to
the two methods of classification for example data 8.1 and 8.2
Table 8.5
Inclusive and exclusive method of classifica-
tion of data
Inclusive method Exclusive method a
ETL Classes Frequency Yield classes Frequency
4-6 10 10-20 16
7-9 22 20-30 54
10-12 18 30-40 14
13-15 13 40-50 11
16-18 17 50-60 10
19-21 10 60-70 10
22-24 7 70-80 8
25-27 3 80-90 7
a Upper limits are not included in a particular class
Example 8.1
Example 8.2
Formula
N
Class
N
Class
Yule
130
8.44 ¼ 8
100
7.91 ¼ 8
Struge
130
8.02
¼
8
100
7.64
¼
8
While deciding the number of classes or
groups, the general idea is to have minimum
variations among the observations of a par-
ticular class/group and maximum variation
among the groups/classes.
Following the above guidelines and the
formulae given below, classes may be formed.
1.
1/4
Table 8.6 Making continuous classes fromdiscrete classes
Yule formula
:
K ¼
2.5
N
2.
Sturge formula
:
K ¼
1 + 3.322 log 10 N
,
ETL classes
Discrete
where
N
is the number of observations and
K
Continuous
Frequency
is the number of classes.
Thus, according to the above two formulae,
the number of classes for Example 8.1 and
Example 8.2 is given in Table 8.4 .
Generally, the range of date can be extended
in both sides (i.e., at the lower end as well as at
the upper end) so as to (1) make the no. of classes
as a whole number and (2) avoid the class width
as a fraction. For example, in the paddy yield, the
maximum value is 87.5 and the minimum is 12.8.
So to have 8 classes, the class width becomes
9.33, a fraction not advisable for the convenience
of further mathematical calculation. To avoid
this, one can increase the data range in both
sides to 10 and 90, respectively, for the lower
and upper sides,
4-6
3.5-6.5
10
7-9
6.5-9.5
22
10-12
9.5-12.5
18
13-15
12.5-15.5
13
16-18
15.5-18.5
17
19-21
18.5-21.5
10
22-24
21.5-24.5
7
25-27
24.5-27.5
3
the effective tiller per hill, that is, for discrete
variable, both the class limits are included in
the respective class. But for Example 8.1, that
is, for yield variable (a continuous character),
exclusive method of classification has been
used.
May it be discrete or continuous, different
statistical measures in subsequent analysis of
the data may result in a fractional form. As
such, generally discrete classes are made continu-
ous by subtracting “
thus making the (90
10)/
¼
8
10 class width a whole number. It should
emphatically be noted that making the class
width whole number is not compulsory; one can
very well use a fractional class width also.
d
/2” from the lower class limit
and adding “
d
/2” to the upper class limit, where
8.1.3.1 Method of Classification
When both the upper limit and lower limit of a
particular class are included in the class, it is
known as
” is the difference between the upper limit of a
class and the lower limit of the following class.
The above classification wrt ETL may be
presented in the form given in Table 8.6 .
Thus, the constructed class limits are known
as lower class boundary ( 3.5 , 6.5 , ... , 24.5 ) and
upper class boundary
d
method of classification.
While in other methods one of these limits is
not included in the respective class, it is known
as
inclusive
method of classification (Table 8.5 ).
The above two classifications, that is, the
inclusive method of classification and the exclu-
sive method of classification, are for Examples
8.2 and 8.1, respectively. For Example 8.2 of
exclusive
), respec-
tively, in case of continuous distribution. The
class
(
6.5
,
9.5
,
...
,
27.5
is equal to the
difference between the upper class boundary and
the lower class boundary of the class interval.
width or the class interval
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